 We proposed a functional theory for targeting low-lying excitation energies of bisonic quantum systems using the one particle picture. We extended the Rayleigh Ritz variational principle to ensemble states with spectrum W and proved a generalized version of the Hohenberg cone theorem. To overcome the V-representability problem common to functional theories, we used the Levi-Liet constrained search formalism combined with an exact convex relaxation. This revealed a complete hierarchy of bisonic exclusion principle constraints analogous to Paul's exclusion principle for fermions. This article was authored by Julia Liebert and Christian Schilling.